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Consider the 2D motion of a rocket of mass in an elliptical orbit around the Earth. The attractive force that the Earth induces on the rocket is directed towards the center of the Earth and has a magnitude of where is the radius of the Earth, is the distance of the rocket from the center of the Earth, and is the acceleration due to gravity on the surface of the Earth.  Choose the correct equations of motion of the rocket. Mark all answers that are correct.

Two rotating rods are connected through a slider block D. At the instant shown, the rod attached at B rotates with an angular velocity

An airplane is used to drop water on brushfires. It is flying horizontally in a straight line with a velocity of  and at an altitude of above the ground.  Determine the distance at which the pilot should release the water so that it will hit the fire at B.  Use .

A uniform slender bar of length is initially vertical and at rest. Its upper end A is attached to a small roller constrained to move along a smooth horizontal surface (i.e., no friction). A horizontal force of  is suddenly applied to the roller as shown. Neglect the mass and size of the roller.  What is the angular acceleration of the bar immediately after the force is applied? 

A sliding panel is supported by two rollers and attached to a counterweight . The system starts from rest. Neglect friction. What is the acceleration of the panel immediately after the system is released?  Use .

The system shown below starts at rest. Neglect the weight of the pulley and friction.  Determine the speed of block A after it has moved a distance of . Use . Enter a number correct to 2 decimal places and in units of .The answer will be between  and .

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